论文标题
Fano Hyperfaces的平衡有理曲线和最小的合理联系
Balanced rational curves and minimal rational connectedness of Fano hypersurfaces
论文作者
论文摘要
在投影空间中的一般狂热性高表面上，我们通过一般的$ k $点的一般集合确定了无限的$ k $最小值$ e $的理性曲线。在索引1的高度表面的情况下，我们的所有$ k \ geq 1 $ $。在附录中Chang证明了一个算术结果，这意味着在索引$> 1 $的情况下，我们方法所涵盖的曲线学度$ E $的密度约为$ \ frac {（n-d）（d- \ frac {5} {2} {2} {2} {2}）}} {（n-2）d} $。
On a general Fano hypersurface in projective space, we determine for infinitely many $k$ the minimal degree $e$ of a rational curve through a general collection of $k$ points. In the case of a hypersurface of index 1, our results hold for all $k\geq 1$. In an appendix, M.C. Chang proves an arithmetical result which implies that in the case of index $>1$, the density of the set of curve degrees $e$ covered by our method is approximately $\frac{(n-d)(d-\frac{5}{2})}{(n-2)d}$.
